Case study in Portfolio Optimization
Open Access
- Author:
- Govindaprasad, Sreenidhi
- Area of Honors:
- Industrial Engineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Dr. Arunachalam Ravindran, Thesis Supervisor
Harriet Black Nembhard, Thesis Honors Advisor - Keywords:
- portfolio optimization
sharpe's model
markowitz model
mutual funds
industrial engineering
financial engineering - Abstract:
- This thesis deals with investment portfolio selection problems. The goal is to determine an optimal investment policy. The securities chosen are 20 Vanguard mutual funds. Return values from the mutual funds over a 10-year period from 2004 to 2014 were collected, together with beta values of the funds using Morningstar.com. Standard deviation of return of the funds and the covariance between funds were calculated. The Sharpe’s bi-criteria linear programming model and Markowitz’s bi-criteria quadratic programming model are used to maximize return while minimizing risk for portfolios of a given risk or return level. Beta values were used to represent risk in the Sharpe’s Model while variance-covariance matrix was used to represent risk in the Markowitz Model. For each model, maximum return and minimum risk portfolios were determined. Efficient frontier connecting the various efficient portfolios was drawn and 8 efficient portfolio options with different return and risk values were presented for an investor to choose from. It was found that as portfolio return increased, risk of investing in the portfolio increased as well. This is because return and risk are conflicting objectives. The efficient portfolios are different depending on the type of investor. A conservative investor intending to minimize risk invested in a portfolio with low risk and accepted a low return. An aggressive investor invested in a portfolio with high return without much consideration to the risk. Within portfolios, it was observed that funds with a lower beta risk and lower standard deviation values were often chosen over funds that had higher risk for the same return. This helps to maximize return while minimizing risk. As the risk of a portfolio increased, funds that provided greater returns were chosen. Covariance was an additional component of risk in the Markowitz Model. When 2 funds had lower covariance between each other, overall risk of the portfolio decreased. It was found that the standard deviation of a portfolio in the Markowitz Model could be reduced to some extent by choosing a diverse group of funds that have low covariance between each other. The beta risk of a portfolio in the Sharpe’s Model can be reduced by choosing funds with lower beta values.